We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, 𝒜t(G) of finite injective dimension, a homology theory π∗𝒜t taking values in 𝒜t(G) based on the homology of the Borel construction, and a finite Adams spectral sequence
Ext𝒜t(G)∗ , ∗ (π∗𝒜t(X), π∗𝒜t(Y)) → [X,Y]∗G
for rational G-spectra X and Y.
This approach should be viewed as an analogue of the Cousin complex in algebraic geometry. It is expected that a similar method will apply to other tensor triangulated categories with finite-dimensional Noetherian Balmer spectra.
This talk relates to this arXiv paper.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
